How can I make this airfoil/wing with the help of a Bezier curve without having to turn it into a mesh in Blender 2.79b?
Unfortunately you cannot model complex shapes in Blender using curves(with handles) only without any add-ons. It is possible to use NURBS, but NURBS surface curves do not have handles on their points. 

There is however an add-on Animation Nodes that provides more procedural modelling functionality and you could construct a surface out of curve splines using loft function. This way you could keep the curves and their handles that influence the shape of the surface. These would be the nodes needed: